HSBC/Markit services sector PMI fell to 50.9 in December from 52.5 in November.
Asian shares fell on Monday after growth in China's services sector slowed sharply last month.
China's CSI300 index dropped 2.3pc to a five-month low after the HSBC/Markit services sector Purchasing Managers' Index fell to 50.9 in December from 52.5 in the previous month, with new business expansion the slowest in six months.
The official non-manufacturing PMI released by the National Bureau of Statistics (NBS) and the China Federation of Logistics and Purchasing (CFLP) on January 3 also dropped for the second month in a row in December, due to a slowdown in construction and service sectors.
Hongbin Qu, HSBC's chief economist for China, said: "Despite the moderation of the headline China Services PMI index, which reflected slower new business growth, labour market conditions improved for the fourth month in a row. We expect the steady expansion of manufacturing sectors to lend support to service sector growth."
Japan's Nikkei, which jumped 57pc in 2013 helped by massive government stimulus, fell heavily to close down 2.35pc, or 382.43 points, at 15,908.88 on the first day of trading in 2014. it is the worst one-day fall in two months.
Hong Kong's Hang Seng fell 0.4pc and Sydney lost 0.47pc. South Korea's Kospi was the one riser among major Asian markets, gaining 0.4pc.
The dollar hovered near a four-week high, supported by an upbeat outlook for the US economy from US Fed Chairman Ben Bernanke that raised expectations that the central bank's massive stimulus will be cut even faster. Investors are looking ahead to Friday's US nonfarm payrolls data which will give further clues as to how well the US economy is recovering and how fast the Fed will unwind quantitative easing.
QE has been a major driver for stock markets. However, Guy Stear, Asian credit and equity strategist at Societe Generale in Hong Kong, said: "The focal point of the Asian markets is more on Chinese growth and on Chinese political situation and how it's going to pan out this year, rather than worrying about how tapering will affect Asia specifically."
